A group of parents and lay faculty members at Immaculata Preparatory School announced yesterday that they intend to continue the school under a private board, although not necesarily at its present site, which an order of Catholic nuns plans to sell.

Archbishop James A. Hickey said he supports efforts to maintain the 79-year-old school, but again indicated that he would not try to block the sale of its campus at Tenley Circle NW to American University.

The support group, Save Immaculata/Dunblane Inc., said it also will operate Immaculata Dunblane School, a grammar school and junior high that shares the 8.2-acre property with the senior high. The schools have about 560 students.

Hickey and the Save Immaculata group made their announcements in a joint statement issued yesterday by the Catholic Archdiocese of Washington, which Hickey heads.

On Friday the supporters of Immaculata filed a lawsuit against the Sisters of Providence, seeking to block the sale on the grounds that the nuns were attempting to use the property improperly for their "personal enrichment."

The nuns had announced Oct. 2 that they would sell the campus at Wisconsin and Nebraska avenues NW to American University for $7.6 million in June 1986 to provide funds for retirement and medical care for their elderly members.

Yesterday's statement said: "Hickey acknowledged both the need of the Sisters to make adequate provision for their aged and infirm [members] as well as the right of parents to defend what they perceive to be their interests in the continuation of [the school] at the present site. It is his desire that both purposes be achieved by mutual agreement."

The statement added that "every effort will be made to allow the present student body to continue their education together," even if necessary at a "temporary alternate site," and to admit a freshman class to the school next September.

At the headquarters of the religious order in St. Mary-of-the-Woods, Ind., Sister Ann Doherty, general superior of the order, said that she had spoken to Hickey by telephone on Saturday and was "very grateful for [his] efforts to create a climate of reconciliation."

She said the order's governing council will reply to yesterday's statement in about two weeks, but added: "We have a binding contract with American University and we are still very serious about that."

The nuns have denied the accusations by the school's supporters.

Yesterday James Spelman, head of the Save Immaculata committee and president of the Immaculata Fathers' Club, said his group has raised about $100,000 and has offered to purchase the school property on terms that "would leave the sisters in exactly the same financial position" as the planned sale to American University.

If the nuns continue to reject this offer, Spelman said, the group could operate the schools elsewhere. He said almost all of the schools' 48 lay teachers have agreed to work for the new venture, along with some of the seven nuns. Hickey said that the archdiocese would help find an altenate site and might "cosponsor. . . a reasonable lease agreement."